Distillation of Binary Mixture Bottom plate and re-boiler For constant molal over flow, and used to denote low rates m-1 m Bottom plate m+1 B xB Re-boiler xm+1 yr Re-boiler plate xB ChE 334: Separation Processes Dr Saad Al-Shahrani

Binary Multistage Distillation The vapor leaving the partial re-boiler is assumed to be in equilibrium with the liquid bottom product. Equilibrium line Operating line ym ym+1 a b a, b,d bottom plate c, d, e Re-boiler plate The operating line for stripping section crosses the diagonal at point (xB , xB( and its slope= yr c d xB e xB xm+1 xm Xm-1 Note: Re-boiler acts as an ideal plate ChE 334: Separation Processes Dr Saad Al-Shahrani

Binary Multistage Distillation Feed plate A feed plate is the plate over which the feed is admitted. The liquid rate over the vapor rate or both may change, depending on the thermal conditions of the feed. Consider the 5 possible feed conditions shown in the next figures which assumes that the feed has been flashed adiabatically to feed stage pressure. F L a. sub-cooed liquid feed: ChE 334: Separation Processes Dr Saad Al-Shahrani

Binary Multistage Distillation As a result of this, flow of liquid in stripping section increases and flow of vapor in rectifying section decreases b. Feed is saturated liquid (bubble point liquid feed) : L F ChE 334: Separation Processes Dr Saad Al-Shahrani

Binary Multistage Distillation C. Partial vaporized feed : L F The liquid portion of feed becomes liquid and the vapor portion of feed becomes vapor = LF+VF ChE 334: Separation Processes Dr Saad Al-Shahrani

Binary Multistage Distillation d. saturated vapor feed (dew point vapor feed) : L F e. Superheated vapor feed F L ChE 334: Separation Processes Dr Saad Al-Shahrani

Binary Multistage Distillation Cold feed q > 1.0 Feed at bubble point (sat. liq.), q=1.0 Feed partially vapor, 0 < q < 1.0 Feed at dew point (sat. vap.), q = 0 Feed superheated vapor, q < 0 ChE 334: Separation Processes Dr Saad Al-Shahrani

McCabe Thiele Graphical Equilibrium-Stage q for sub-cooled feed (Tb > TF) L F ChE 334: Separation Processes Dr Saad Al-Shahrani

McCabe Thiele Graphical Equilibrium-Stage q for superheated feed (TF > Td) Boiling liquid L F TF= feed temperature Tb, Td= bubble and dew point of feed respectively. = average latent heat of vaporization CpL, CpV = specific heat of liquid and vapor respectively. ChE 334: Separation Processes Dr Saad Al-Shahrani

McCabe Thiele Graphical Equilibrium-Stage Feed line The contribution of the feed stream to the internal flow of liquid = qF The total flow rate of liquid in the stripping section is: and e.g For saturated liquid feed For saturated vapor feed ChE 334: Separation Processes Dr Saad Al-Shahrani

McCabe Thiele Graphical Equilibrium-Stage The contribution of the feed stream to the internal flow of vapor =F(1- q) The total flow rate of vapor in the rectifying section is: , e.g For saturated liquid feed , For saturated vapor feed ChE 334: Separation Processes Dr Saad Al-Shahrani

McCabe Thiele Graphical Equilibrium-Stage For constant molal over flow Rectifying section V yn L xn+1 n n+1 stripping section m+1 ym xm+1 m ChE 334: Separation Processes Dr Saad Al-Shahrani

McCabe Thiele Graphical Equilibrium-Stage To locate the point where the operating lines intersect, Let yn=ym , xn+1=xm+1 and subtract equation (1) from equation (2) FxF Feed line q-line ChE 334: Separation Processes Dr Saad Al-Shahrani

McCabe Thiele Graphical Equilibrium-Stage This equation represents a straight line, called the feed line on which all intersections of operating lines must fall. The position of feed line depend on xF and q. Its slope is and its intercept is This line cross the diagonal at x= xF ChE 334: Separation Processes Dr Saad Al-Shahrani

McCabe Thiele Graphical Equilibrium-Stage ra cold liquid q > 1 slope + rb saturated liquid q = 1 slope  rc (vap. + liq.) 0 < q < 1 slope - rd saturated vapor q = 0 slope 0 re superheated q < 0 slope + XD q =1 q >1 0 < q <1 b a c q =0 d r y e q <1 XB XB XF XD x ChE 334: Separation Processes Dr Saad Al-Shahrani

McCabe Thiele Graphical Equilibrium-Stage Construction of operating lines Locate the feed line ( ) according to the feed conditions. Locate the rectifying line ( ). This line croces the diagonal at (xD, xD) and of intercept ( ) Draw the stripping line through point (xB, xB( an the intersection of rectifying line with the feed line. Note: xF, xB , xD, L,D are constant ChE 334: Separation Processes Dr Saad Al-Shahrani

McCabe Thiele Graphical Equilibrium-Stage Plate Feed Location The feed plate is always represented by the triangle that has one corner on the rectifying line and one on the stripping line y XD XF XB a b c x Note: The number of plates = number of plates + re-boiler plate. The liquid on the feed plate does not have the same composition as the feed. ChE 334: Separation Processes Dr Saad Al-Shahrani

1 2 3 4 Feed line 5 R.O. L 6 7 8 . 9 S.O. L 10 R xF xD xB

McCabe Thiele Graphical Equilibrium-Stage Heating and cooling requirements D xD Liq. At its bubble point temperature Va Vap. at its dew point temp. Top plate La xa T1 T2 Heat loss from a large insulated is relatively small. For condenser a. If the condensate is not su-bcooled (at Tbub)  molal latent heat of vaporization of more volatile component ChE 334: Separation Processes Dr Saad Al-Shahrani

McCabe Thiele Graphical Equilibrium-Stage b. If Su-cooled Reflux If the reflux is cooled below the bubble point, a portion of vapor coming to the top plate (1) must condensed to heat the reflux ΔL that is condensed inside the column is obtained from: D xD V Top plate L Tc T1 ΔL Cpc=specific heat of condensation T1= temp. of liq. On to plate bubble point of condensate Tc= temp. of return condensate (reflux) c= heat of vaporization of condensate for volatile component. ChE 334: Separation Processes Dr Saad Al-Shahrani

McCabe Thiele Graphical Equilibrium-Stage The actual reflux ratio in the column is T1 Tbc= bubble point of the condensate ChE 334: Separation Processes Dr Saad Al-Shahrani

McCabe Thiele Graphical Equilibrium-Stage For re-boiler Bottom plate condensate B xB steam = steam consumption = vapor flow rate from re-boiler s = latent heat of steam.  = molal latent heat of mixture at the bottom  molal latent heat of less volatile component ChE 334: Separation Processes Dr Saad Al-Shahrani